Super Mario Bros. 3
--This introduced the themed environment ideas to the franchise, had a ton of cool power ups, and was one of the most well polished games on the system. Perhaps the best platformer ever made.
The Legend of Zelda: Ocarina of Time
--Majora's Mask had a fantastically grim atmosphere, and its design turned the game into one giant puzzle. Wind Waker actually felt like an adventure, which is something most adventure games fail to deliver. Twilight Princess takes the idea of Ocarina's formula and applies it on a much larger scale (Twilight Princes is to Ocarina as Link to the Past is to The Legend of Zelda). However, Ocarina of Time felt like the best package in the entire series--the story, size, gameplay--it is all perfect. Truly, a timeless classic.
Shadow of the Colossus
--It takes a lot of talent to make a game about sword fighting, horseback riding, archery (which works while riding the horse), and climbing vine-covered walls without reducing itself to an Ocarina rip-off. Sure, it's easy to tell Ocarina was the biggest gameplay influence, but the presentation and basic idea is so different. The world is vast, but empty. There are no dungeons or towns. There's really no reason to explore other than wanting to see a beautiful, secluded world. The entire design is minimalistic; the gameplay is composed entirely of climbing, running, swording, bowing, and horsing, and it has a "draw your own conclusions" type of story. This is one of the few examples of minimalistic story-telling that I actually enjoyed, and although the gameplay should have been a lot tighter, it is one of the best experiences offered in gaming.
Sweet Home
--The only game on my list you may not have heard of. This is an 8-bit survival horror RPG that was released on the Famicon in 1989 on the same day as the film it was based on. Being an early licensed game that was actually good, it should be no surprise that Capcom was behind this game. It is pretty much the predecessor to Resident Evil, and I find Sweet Home to be the better experience. The story has a very sudden pacing. This happens because most of it is delivered through notes and hidden messages that the party finds throughout the mansion. This leads to many shocking developments as the story gets darker and darker. With its grim story and gore, this game could have easily earned an M rating, and unlike most M's, it would live up to the word "mature".
Chrono Trigger
--Hopefully, most of you have played this one. It has a fantastic combat system that lets your characters work together. While the story may not sound impressive on paper, it's how they build it up that I love. Each era has its own little sub-plot that build up into one great whole. Although I do not think it's the best game on this list, it is my favorite game of all time. Hmm...maybe I should have saved my time pun for this one. Oh well, it worked just as well with Ocarina.